Next Session

Monday, November 10, 2025 at UCLA. Talks are in the Mathematical Sciences Building, MS 6221. 

2:30 - 3:30 pm: Informal Meet & Greet at the Kerckhoff Coffee House

3:30 – 4:20 pm: Dylan Possamaï (ETH Zurich)

Stackelberg games and stochastic targets

In this talk, we provide a general approach to reformulating any continuous-time stochastic Stackelberg differential game under closed-loop strategies as a single-level optimisation problem with target constraints. More precisely, we consider a Stackelberg game in which the leader and the follower can both control the drift and the volatility of a stochastic output process, in order to maximise their respective expected utility. The aim is to characterise the Stackelberg equilibrium when the players adopt “closed-loop strategies”, i.e. their decisions are based solely on the historical information of the output process, excluding especially any direct dependence on the underlying driving noise, often unobservable in real-world applications. We first show that, by considering the second-order-backward stochastic differential equation associated with the continuation utility of the follower as a controlled state variable for the leader, the latter’s unconventional optimisation problem can be reformulated as a more standard stochastic control problem with stochastic target constraints. Thereafter, adapting the methodology developed by Soner and Touzi or Bouchard, Elie, and Imbert, the optimal strategies, as well as the corresponding value of the Stackelberg equilibrium, can be characterised through the solution of a well-specified system of Hamilton-Jacobi-Bellman equations. For a more comprehensive insight, we illustrate our approach through a simple example, facilitating both theoretical and numerical detailed comparisons with the solutions under different information structures studied in the literature.

This is a joint work with Camilo Hernández, Nicolás Hernández Santibánez, and Emma Hubert.

4:30 – 5:20 pm: Marco Frittelli (Milano University)

Collective Phenomena in Financial Markets: Arbitrage, No Free Lunch, Individual Rationality.

This talk investigates the role of cooperation and interaction among agents in financial markets, exploring how collective action redefines fundamental theoretical concepts.

A cornerstone of this approach is the concept of Collective Arbitrage and Collective Super-replication, as introduced by Biagini et al. [1] in a discrete-time setting. This work demonstrates that effective risk-sharing significantly reduces hedging costs, thereby necessitating the No Collective Arbitrage (NCA) condition as a crucial extension of the standard no-arbitrage principle.

We then discuss the generalization of this framework to continuous-time semimartingale markets [2], which requires the introduction of a No Collective Free Lunch condition.

Moreover, by assuming heterogeneous, monotone concave preferences, we show that the resulting collective exchanges are strictly beneficial for all participating agents in the market. This finding confirms that cooperation not only removes systemic arbitrage opportunities but serves as a powerful source of individual utility gain.

References:

[1] Biagini, F., Doldi, A., Fouque, J-P., Frittelli, M. and Meyer-Brandis T. (2025). Collective Arbitrage and the Value of Cooperation. Forthcoming in Finance and Stochastics.

[2] Frittelli, M. (2025). Collective Free Lunch and the FTAP. SIAM Journal of Financial Mathematics, Vol. 16, No. 1, pp. 53–67.

[3] Doldi, A., Frittelli, M. and Maggis, M. (2025). Collective completeness and pricing hedging Duality. Math. Fin. Econ.

5:30 – 5:50 pm: Georg Menz (UCLA)

From portfolio rebalancing to non-conservative optimal transport

We will open this talk with considering the question how should an investor rebalance their portfolio holding if the current position differs from the investment target. We will use this portfolio rebalancing problem as a motivation for introducing a new variant of optimal transport.

Since the current as well as the target portfolio positions correspond to probability distributions, the question of how to rebalance naturally relates to optimal transport. However, in presence of bid-ask spread, part of the portfolio value is lost in executing the rebalancing trades. Therefore, the classical OT framework does not quite capture the rebalancing problem.

Instead, we will introduce a framework where the mass can be lost (or gained) during the transport. We will refer to it as non-conservative optimal transport. Existence of transport plans as well as maps, and strong duality can be shown.

6:00 – 6:20 pm: Zihao Gu (USC)

On information controls

In this talk, we investigate an optimization problem where the information serves as the control variable. More precisely, the control takes the form of a sub-$\sigma$-algebra of a given $\sigma$-algebra, or a sub-filtration of a given filtration. We discuss an insider trading problem as a motivating example, and present preliminary results in a continuous-time dynamic framework. We develop an Itô's formula for smooth functions defined on $\mathcal{P}_2(\mathbb{R}^d)$, the space of laws of random probability measures on $\mathbb{R}^d$. This result leads naturally to a Hamilton–Jacobi–Bellman (HJB) equation on this space, which characterizes the dynamic value function of the information control problem. The talk is based on an ongoing joint work with Jianfeng Zhang.

Dinner: California Pizza Kitchen at Westwood, 1001 Broxton Ave. We will walk there together after the Forum (approximately a 10-15 minute walk).